chore(deps): bump azure-identity from 1.23.1 to 1.25.1 (#14877)

Bumps [azure-identity](https://github.com/Azure/azure-sdk-for-python) from 1.23.1 to 1.25.1.
- [Release notes](https://github.com/Azure/azure-sdk-for-python/releases)
- [Changelog](https://github.com/Azure/azure-sdk-for-python/blob/main/doc/esrp_release.md)
- [Commits](https://github.com/Azure/azure-sdk-for-python/compare/azure-identity_1.23.1...azure-identity_1.25.1)

---
updated-dependencies:
- dependency-name: azure-identity
  dependency-version: 1.25.1
  dependency-type: direct:production
  update-type: version-update:semver-minor
...

Signed-off-by: dependabot[bot] <support@github.com>
Co-authored-by: dependabot[bot] <49699333+dependabot[bot]@users.noreply.github.com>

uv.lock

@@ -212,7 +212,7 @@ wheels = [
 
 [[package]]
 name = "azure-identity"
-version = "1.23.1"
+version = "1.25.1"
 source = { registry = "https://pypi.org/simple" }
 dependencies = [
     { name = "azure-core" },
@@ -221,9 +221,9 @@ dependencies = [
     { name = "msal-extensions" },
     { name = "typing-extensions" },
 ]
-sdist = { url = "https://files.pythonhosted.org/packages/b5/29/1201ffbb6a57a16524dd91f3e741b4c828a70aaba436578bdcb3fbcb438c/azure_identity-1.23.1.tar.gz", hash = "sha256:226c1ef982a9f8d5dcf6e0f9ed35eaef2a4d971e7dd86317e9b9d52e70a035e4", size = 266185, upload-time = "2025-07-15T19:16:38.077Z" }
+sdist = { url = "https://files.pythonhosted.org/packages/06/8d/1a6c41c28a37eab26dc85ab6c86992c700cd3f4a597d9ed174b0e9c69489/azure_identity-1.25.1.tar.gz", hash = "sha256:87ca8328883de6036443e1c37b40e8dc8fb74898240f61071e09d2e369361456", size = 279826, upload-time = "2025-10-06T20:30:02.194Z" }
 wheels = [
-    { url = "https://files.pythonhosted.org/packages/99/b3/e2d7ab810eb68575a5c7569b03c0228b8f4ce927ffa6211471b526f270c9/azure_identity-1.23.1-py3-none-any.whl", hash = "sha256:7eed28baa0097a47e3fb53bd35a63b769e6b085bb3cb616dfce2b67f28a004a1", size = 186810, upload-time = "2025-07-15T19:16:40.184Z" },
+    { url = "https://files.pythonhosted.org/packages/83/7b/5652771e24fff12da9dde4c20ecf4682e606b104f26419d139758cc935a6/azure_identity-1.25.1-py3-none-any.whl", hash = "sha256:e9edd720af03dff020223cd269fa3a61e8f345ea75443858273bcb44844ab651", size = 191317, upload-time = "2025-10-06T20:30:04.251Z" },
 ]
 
 [[package]]